Nonclassical trajectories in head-on collisions

A. Kumar1,2, T. Krisnanda2, P. Arumugam1, and T. Paterek2,3,4

1Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, India
2School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
3Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland
4MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Rutherford scattering is usually described by treating the projectile either classically or as quantum mechanical plane waves. Here we treat them as wave packets and study their head-on collisions with the stationary target nuclei. We simulate the quantum dynamics of this one-dimensional system and study deviations of the average quantum solution from the classical one. These deviations are traced back to the convexity properties of Coulomb potential. Finally, we sketch how these theoretical findings could be tested in experiments looking for the onset of nuclear reactions.

The unavoidable existence of a finite momentum variance implies that quantum mechanical wave packets cannot be stopped completely. Therefore the situations where classical particles stop, like head-on collisions, are natural candidates to probe the emergence of nonclassicality. We demonstrate this phenomenon in the paradigmatic Rutherford scattering experiment.

► BibTeX data

► References

[1] H. Geiger and E. Marsden, Proceedings of the Royal Society A 82, 495 (1909).
https:/​/​doi.org/​10.1098/​rspa.1909.0054

[2] E. Rutherford, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 21, 669 (1911).
https:/​/​doi.org/​10.1080/​14786440508637080

[3] C. J. Joachain, Quantum Collision Theory (North-Holland Publishing Company, Amsterdam-Oxford, 1975).

[4] P. Ehrenfest, Zeitschrift für Physik 45, 455 (1927).
https:/​/​doi.org/​10.1007/​BF01329203

[5] B. C. Hall, Quantum Theory for Mathematicians, 1st ed. (Springer-Verlag, New York, USA, 2013). 10.1007/​978-1-4614-7116-5.
https:/​/​doi.org/​10.1007/​978-1-4614-7116-5

[6] M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, USA, 1966).

[7] R. dE. Atkinson and F. G. Houtermans, Zeitschrift für Physik 54, 656 (1929).
https:/​/​doi.org/​10.1007/​BF01341595

[8] A. S. Eddington, Nature 106, 14 (1920).
https:/​/​doi.org/​10.1038/​106014a0

[9] L. A. MacColl, Physical Review 40, 621 (1932).
https:/​/​doi.org/​10.1103/​PhysRev.40.621

[10] V. V. Dodonov, A. B. Klimov, and V. I. Man'ko, Physics Letters A 220, 41 (1996).
https:/​/​doi.org/​10.1016/​0375-9601(96)00482-3

[11] B. B. Kadomtsev and M. B. Kadomtsev, Physics Letters A 225, 303 (1997).
https:/​/​doi.org/​10.1016/​S0375-9601(96)00804-3

[12] M. A. Andreata and V. V. Dodonov, Journal of Physics A: Mathematical and General 37, 2423 (2004).
https:/​/​doi.org/​10.1088/​0305-4470/​37/​6/​031

[13] A. V. Dodonov and V. V. Dodonov, Physics Letters A 378, 1071 (2014).
https:/​/​doi.org/​10.1016/​j.physleta.2014.02.016

[14] R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed. (John Wiley & Sons, New York, USA, 1985).

[15] J. L. W. V. Jensen, Acta Mathematica 30, 175 (1906).
https:/​/​doi.org/​10.1007/​BF02418571

[16] A. Askar and A. S. Cakmak, The Journal of Chemical Physics 68, 2794 (1978).
https:/​/​doi.org/​10.1063/​1.436072

[17] Z. Sun and W. Yang, The Journal of Chemical Physics 134, 041101 (2011).
https:/​/​doi.org/​10.1063/​1.3549570

[18] F. J. Vesely, Computational Physics, 2nd ed. (Springer, New York, USA, 2001). 10.1007/​978-1-4615-1329-2.
https:/​/​doi.org/​10.1007/​978-1-4615-1329-2

[19] S. Majorosi and A. Czirják, Computer Physics Communications 208, 9 (2016).
https:/​/​doi.org/​10.1016/​j.cpc.2016.07.006

[20] M. A. Doncheski and R. W. Robinett, European Journal of Physics 20, 29 (1999).
https:/​/​doi.org/​10.1088/​0143-0807/​20/​1/​009

[21] M. Andrews, American Journal of Physics 66, 252 (1998).
https:/​/​doi.org/​10.1119/​1.18854

[22] A. Goldberg, H. M. Schey, and J. L. Schwartz, American Journal of Physics 35, 177 (1967).
https:/​/​doi.org/​10.1119/​1.1973991

[23] M. Belloni, M. A. Doncheski, and R. W. Robinett, Physica Scripta 71, 136 (2005).
https:/​/​doi.org/​10.1238/​Physica.Regular.071a00136

[24] H. A. Kramers, Zeitschrift für Physik 39, 828 (1926).
https:/​/​doi.org/​10.1007/​BF01451751

[25] G. Wentzel, Zeitschrift für Physik 38, 518 (1926).
https:/​/​doi.org/​10.1007/​BF01397171

[26] M. Selmke and F. Cichos, American Journal of Physics 81, 405 (2013).
https:/​/​doi.org/​10.1119/​1.4798259

[27] N. Wheeler, Remarks concerning the status & some ramifications of EHRENFEST'S THEOREM (1998).

[28] W. Żakowicz, Acta Physica Polonica B 33, 2059 (2002a).

[29] W. Żakowicz, Acta Physica Polonica A 101, 369 (2002b).
https:/​/​doi.org/​10.12693/​APhysPolA.101.369

[30] J. J. V. Maestri, R. H. Landau, and M. J. Páez, American Journal of Physics 68, 1113 (2000).
https:/​/​doi.org/​10.1119/​1.1286310

[31] P. J. A. Buttle and L. J. B. Goldfarb, Nuclear Physics 78, 409 (1966).
https:/​/​doi.org/​10.1016/​0029-5582(66)90617-1

[32] W. von Oertzen, Nuclear Physics A 148, 529 (1970).
https:/​/​doi.org/​10.1016/​0375-9474(70)90646-9

[33] B. Imanishi and W. von Oertzen, Physics Reports 155, 29 (1987).
https:/​/​doi.org/​10.1016/​0370-1573(87)90101-3

[34] J. M. Sparenberg, D. Baye, and B. Imanishi, Physical Review C 61, 054610 (2000).
https:/​/​doi.org/​10.1103/​PhysRevC.61.054610

[35] S. Edwards, Nuclear Physics 47, 652 (1963).
https:/​/​doi.org/​10.1016/​0029-5582(63)90911-8

[36] K. Ogata, M. Kan, and M. Kamimura, Progress of Theoretical Physics 122, 1055 (2009).
https:/​/​doi.org/​10.1143/​PTP.122.1055

[37] P. Descouvemont, Physics Letters B 772, 1 (2017).
https:/​/​doi.org/​10.1016/​j.physletb.2017.06.024

[38] M. Liao, R. Grenier, Q.-D. To, M. P. de Lara-Castells, and C. Léonard, Journal of Physical Chemistry C 122, 14606 (2018).
https:/​/​doi.org/​10.1021/​acs.jpcc.8b03555

[39] S. M. Nejad, S. Nedea, A. Frijns, and D. Smeulders, Micromachines 11, 319 (2020).
https:/​/​doi.org/​10.3390/​mi11030319

[40] R. Grenier, Q.-D. To, M. P. d. Lara-Castells, and C. Léonard, Journal of Physical Chemistry A 119, 6897 (2015).
https:/​/​doi.org/​10.1021/​acs.jpca.5b03769

[41] I. Galbraith, Y. S. Ching, and E. Abraham, American Journal of Physics 52, 60 (1984).
https:/​/​doi.org/​10.1119/​1.13811

[42] C. A. Bertulani, Few-Body Systems 56, 727 (2015).
https:/​/​doi.org/​10.1007/​s00601-015-0990-z

[43] S. Bacca and H. Feldmeier, Physical Review C 73, 054608 (2006).
https:/​/​doi.org/​10.1103/​PhysRevC.73.054608

[44] H. S. Park and W. K. Liu, Computer Methods in Applied Mechanics and Engineering 193, 1733 (2004).
https:/​/​doi.org/​10.1016/​j.cma.2003.12.054

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2021-07-28 16:00:58). On SAO/NASA ADS no data on citing works was found (last attempt 2021-07-28 16:00:59).